Is there experimental data that proves that electrons can jump to another level more easily when in close proximity to other atoms as suggested in Volume III - Semiconductors / Band Theory of Solids / Electron Band Overlap in Metallic Elements?

I am not aware of a method where a single atom can be isolated. If such a method exists can someone point me to a paper (or papers) to read?

If the rationale for this assertion is from experiments where various dilutions are involved, how is it known for a certainty that the electrons are actually moving back and forth between sub-levels when multitudes of atoms are in close proximity?

I wrote a long response to this question, and then accidently hit the back button. The more the electron orbital shells of the atoms overlap, the more energy level splitting there will be. However repulsive forces (electron-electron, nucleus-nucleus) will try to keep the atoms apart. There is a balance that can be reached (Lennard-Jones potential) to determine the bond-length.

So is his statement correct? Not really, but I think he was getting at something else. If you bring atoms closer together, then yes there will be more energy level splitting and thus more energy levels, and that makes it very favorable for bonding.

However he doesn't mention the repulsive forces which will also increase in magnitude as you bring two atoms close together. In fact at some point the repulsive force will begin to dominate the attractive force (energy-level splitting). If you could force two atoms together, the system would be in a very high energy state and the two atoms would want to repel eachother. Once you remove the force that keeps the atoms close together, they will repel eachother and move away until the repulsive force becomes less dominant than the attractive force. When the attractive and repulsive forces balance, the system will be in the lowest possible energy.